The plaintiffs argue that the EO violates the separation of powers, the Take Care Clause, and the Administrative Procedure Act, among others. In short:

To repeal two regulations for the purpose of adopting one new one, based solely on a directive to impose zero net costs without any consideration of benefits, is arbitrary, capricious, an abuse of discretion, and not in accordance with law, for at least three reasons. First, no governing statute authorizes any agency to withhold a regulation intended to address identified harms to public safety, health, or other statutory objectives on the basis of an arbitrary upper limit on total costs (for fiscal year 2017, a limit of $0) that regulations may impose on regulated entities or the economy. Second, the Executive Order forces agencies to repeal regulations that they have already determined, through notice-and-comment rulemaking, advance the purposes of the underlying statutes, and forces the agencies to do so for the sole purpose of eliminating costs that the underlying statutes do not direct be eliminated. Third, no governing statute authorizes an agency to base its actions on a decisionmaking criterion of zero net cost across multiple regulations.

The plaintiffs say that the EO violates the separation of powers, because "[b]y requiring agencies engaged in rulemaking to consider and take final action or to withhold final action based on factors that are impermissible and arbitrary under the governing statutes, the Executive Order purports to amend the statutes through which Congress has delegated rulemaking authority to federal agencies." They say it violates the Take Care Clause, because it "directs agencies to take action contrary to numerous laws passed by Congress." (The plaintiffs also bring claims under non-statutory review of ultra vires action, and the APA.)

The plaintiffs point to harms they'll incur under several statutes, if administrative agencies follow the two-for-one rule. Those include the Motor Vehicle Safety Act and Motor Carrier Safety Act, OSHA, the Mine Safety and Health Act, the Toxic Substance Control Act, and several other environmental protection acts.

The plaintiffs point to harms (for standing purposes) throughout, including organizational harms (by requiring the plaintiffs to shift advocacy priorities) and member harms (because a lack of regulation, where a statute requires it, will harm individual members).